We have been given that you drop a ball from a window 50 metres above the ground. The ball bounces to 50% of its previous height with each bounce. We are asked to find the total distance traveled by up and down from the time it was dropped from the window until the 25th bounce.
We will use sum of geometric sequence formula to solve our given problem.
, where,
a = First term of sequence,
r = Common ratio,
n = Number of terms.
For our given problem 
, 
and 
.
Therefore, the ball will travel 100 meters and option B is the correct choice.
Answer:
(x-9)(x²+9x+81); it'll give a difference of cubes
Step-by-step explanation:
Generally, the difference of cubes formula is (a³-b³)=(a-b)(a²+ab+b²), and the third option is the only one which fits it; with "a"= x and "b"= 9.
*The sum of cubes formula is (a³+b³)=(a+b)(a²-ab+b²); for future reference.
<h3>
Answer: </h3><h3>
Yes, the triangles are similar</h3><h3>
AC = 6</h3>
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Explanation:
Focus on triangle ABC. Let's find the missing angle
A+B+C = 180
113+B+22 = 180
B+135 = 180
B = 180-135
B = 45
Between the triangles, have two pairs of angles that are congruent
A = D = 113
B = E = 45
Which is enough to prove the triangles are similar through the angle angle (AA) similarity theorem. This must mean that C = F = 22
Since we have A pair with D, and B pair with E, this means that 
The order of the letters is important so we know how the angles pair up. The first letters pair up together, the second letters pair up, and so on.
Consequently, this means sides BC and EF pair up and AC and DF pair up
We can then say...
BC/EF = AC/DF
18/12 = x/4
18*4 = 12*x
72 = 12x
12x = 72
x = 72/12
x = 6
AC = 6
Equations and Inequalities - Multiplication equations - First Glance. To solve a multiplication equation, use the inverse operation of division. Divide both sides by the same non-zero number. Click the equation to see how to solve it.
Answer:
.3 is greater.
Step-by-step explanation:
.13
.3 or .30
These are the same, and obviously .30 is larger than .13.
